7.1.3 Magnitudes

The phase readings for magnitude determination is described on page .

In SEISAN version 8.3, there are substantial changes in the way amplitudes are read and two new magnitude scales have been added (broad band body and surface wave magnitudes). Furthermore, the Richter attenuation curve is now used be default for the body wave magnitude. The phase names used for amplitudes have also changed. These changes are due to the new standards for magnitude calculation approved by the IASPEI. For more on the application of the different magnitude scales, see Havskov and Ottemöller [2010].

Magnitudes are calculated using coda, amplitude and spectral level. Parameters are given in the station file using the RESET TEST variables. For magnitude based on amplitude, the amplitude must be given in nanometers in the input file (SEISAN standard).

Local magnitude Ml

The formula used to calculate local magnitude is

$$Ml = a * log_{10} (amp) + b*log_{10}(dist) + c*dist + d$$

where a,b,c,d are constants, $log_{10}$ is logarithm to the base 10, amp is maximum ground amplitude (zero $-$ peak) in nm and dist is hypocentral distance in km (RESET TEST 75-78). The default constants are for California [Hutton and Boore, 1987] which gives the following relation

$$Ml = log_{10}(amp) + 1.11 log_{10}(dist) + 0.00189 dist - 2.09$$

It is here assumed that the gain of the Wood-Anderson instrument is $2080$ . An amplitude of $1 mm$ of the Wood Anderson seismogram is then $10^6nm/2080$ and inserting this amplitude above together with a distance of 100 km gives magnitude 3 as originally defined by Richter. It is assumed that the maximum amplitude is picked on a seismogram simulating the original Wood-Anderson seismogram, see program MULPLT. SEISAN uses hypocentral distance, while the original Ml scale used epicentral distance (no deep earthquakes in California). We use hypocentral distance so Ml also can be used for deep earthquakes, but the user should be aware that the Ml relation for deep earthquakes might be different from the relation for shallow earthquakes.

Local magnitudes are only calculated for events with epicentral distance LESS THAN TEST(57) (default 1500 km) and if the period is less than 5.0 secs. All amplitudes for the phases `L', `S ', Sg, SG, AMP, and AML, AMPL, IAML or blank are used. This means that if an amplitude is picked on both Lg and Sg, both will be used. The period is not used. The many possible phase names is a result of changes over time and thus to ensure that Ml is calculated correctly with older data. From version 8.3, MULPLT produces the standard IASPEI name IAML.

Coda magnitude Mc

The coda magnitude is calculated using

$$Mc = a * log_{10}(coda) + b * dist + c$$

where coda is coda length in secs and a,b and are constants (RESET TEST 7-9). If `a' is given as a negative number, the following formula will be used

$$Mc = abs(a)*log_{10}(coda)*log_{10}(coda) + b * dist + c$$

If both Mc and Ml are calculated, Ml is written first on the header line.

Coda magnitude is only calculated if the epicentral distance is less than TEST(57).

Surface wave magnitude Ms

Ms is calculated using the standard

$$Ms = log_{10}(amp/T)+1.66log_{10}(dist)+3.3$$

where T is period. Amplitude is in micrometer and distance in degrees, however in the Nordic format nm and km are used and the program converts. Ms is only calculated if the period is larger than 10.0 seconds in which case the program automatically assumes that Ms is the wanted magnitude. The phase used can be AMS, AMPS, AMP or blank. The current version of MULPLT produces the standard IASPEI name IAMs_20. The many possible phase names are a result of changes over time and thus to ensure that Ms is calculated correctly with older data. It is assumed that the amplitude has been picked on a WWSSN standard LP trace and that the period is in the range $18-22 s$ (see program MULPLT). Ms will be calculated even if the period is outside this range, but it will not be correct according to the standard. The distance range is between TEST(114) and 100 deg. before version 10.5, there were no distance limits. TEST(114)=20 deg by default. Depth must be less than TEST(115). Before version 10.5, there were no depth limit. TEST(115) is 60 km by default.

Broadband surface wave magnitude MS (IASPEI code MS_BB, but SEISAN uses MS for simplicity, new from SEISAN version 8.3)

MS is calculated using the standard

$$MS = log_{10}(amp/T)_{max}+1.66log_{10}(dist)+3.3$$

or

$$MS = log_{10}(V_{max}/2 \pi )+1.66log_{10}(dist)+3.3$$

where $V_{max}$ is the maximum velocity. The IASPEI definition is to use velocity and the period is thus not needed but read for information. The velocity is in micrometer/s and distance in degrees, however in the Nordic format $nm/s$ and $km$ are used and the program converts when calculating magnitudes. MS is only calculated if the period is larger than 3 seconds and less then 60 seconds, distance must be larger than or equal to 222 km (2 degrees) and less or equal to 160 degrees. The depth must be less than TEST(115) (default 60 km). Before version 10.5, there was no check of depth. The phase used to report the amplitude and period must be called IVMs_BB which the current version of MULPLT produces. The biggest advantage using MS compared to Ms, is that any period in the range $2-60 s$ can be used.

Body wave magnitude mb

mb is calculated using

$$mb = log_{10}(amp/T) + Q(dist,depth)$$

where Q is a hardwired function of distance and depth and amp is the amplitude in nm. There are two possibilities: The default (set by REST TEST(108) is the standard Gutenberg and Richter (1956) curve while alternatively the Veith-Clawson curve can be used [Veith and Clawson, 1972]. Before SEISAN version 8.3, Veith-Clawson was always used. mb is only calculated if the epicentral distance is less than or equal to 100 degrees and larger than or equal to TEST(113), default 20 deg (IASPEI standard and SEISAN default is 20 degrees).Before version 10.5, the lower distance was TEST(57) (defualt 1500 km). The period must be smaller than 3 si an dlarger then 0.2 s and the phase is P, AMP, AMb, AMB, AMPB, AMPb, blank character or IAmb. The current version of MULPLT produces the standard IASPEI name IAmb. The many possible phase names are a result of changes over time and thus to ensure that mb is calculated correctly with older data.

Broad band body wave magnitude mB (new from SEISAN version 8.3)

The broad band magnitude mB (official IASPEI name is mB_BB) is calculated using

$$mB = log_{10}(amp/T)_{max} + Q(dist,depth)$$

or

$$mB = log_{10}(V_{max}/2 \pi ) + Q(dist,depth)$$

where $V_{max}$ is the maximum velocity and Q is a hardwired function of distance and depth. The IASPEI standard is to use velocity and SEISAN store the velocity in nm/s. There are two possibilities for the atteneuation function: The default (set by RESET TEST(108) is the standard Gutenberg and Richter (1956) curve while alternatively the Veith-Clawson curve can be used [Veith and Clawson, 1972]. mB is only calculated if the epicentral distance is less than or equal to 100 degrees and larger than or equal to TEST(113) (IASPEI standard and SEISAN default 2 degrees. Before version 10.5, the lower limit was TEST(57), default 1500 km) and the period is larger than 0.2s and less than 30s and the phase name is IVmB_BB . The current version of MULPLT produces the standard IASPEI name IVmB_BB. The biggest advantage using mB compared to mb, is that the mB scale does not saturate before magnitude 8.

Moment magnitude Mw

Mw is calculated as

$$Mw = 2/3 * \Big( log_{10}(moment) - 9.1 \Big)$$

where moment is in Nm (see also section 8.12). When an event is relocated, the moment is also recalculated according to revised hypocentral distance.

NOTE: If an amplitude has a given period between 5 and 10 secs, it is not used for Ml and mb magnitude calculation, see above. If an event is not located, there will normally be no magnitude calculation and all magnitude and distance information is deleted from the output S-file (hyp.out) except, the magnitude in the 3rd position on the header line if it has an agency different from the default agency. The only exception is that if a coda is given, the epicentral distance is retained and coda magnitude will therefore be calculated. This means that for events, which cannot be located, it is still possible to calculate coda magnitudes by manually entering the epicentral distance on the line containing the coda length.

On the first header line, there is room for 3 magnitudes. If there is a magnitude in the 3rd position, it is not overwritten unless the default agency is overwritten, so there will often only be room for 2 calculated magnitudes on the first header line. If more magnitudes are calculated, they will be written on a subsequent hypocenter line, which is identified by having the same year, month, day and hypocenter agency as the first header line. This means that there is room for a total of 6 magnitudes, which can each, be updated when relocating. Hypocenter info and all 6 magnitudes can be printed out on one line with program REPORT.

All magnitudes can have a station dependent correction given in the station file. This correction does not affect the Mc in print.out file. Mb and mB use the same correction and Ms and MS use the same correction. Only calculate magnitude: If TEST(106) is set to 1.0, only magnitudes are calculated, provided a distance is given.